The Rayleigh-Ritz method, refinement and Arnoldi process for periodic matrix pairs

We extend the Rayleigh-Ritz method to the eigen-problem of periodic matrix pairs. Assuming that the deviations of the desired periodic eigenvectors from the corresponding periodic subspaces tend to zero, we show that there exist periodic Ritz values that converge to the desired periodic eigenvalues unconditionally, yet the periodic Ritz vectors may fail to converge. To overcome this potential problem, we minimize residuals formed with periodic Ritz values to produce the refined periodic Ritz vectors, which converge under the same assumption. These results generalize the corresponding well-known ones for Rayleigh-Ritz approximations and their refinement for non-periodic eigen-problems. In addition, we consider a periodic Arnoldi process which is particularly efficient when coupled with the Rayleigh-Ritz method with refinement. The numerical results illustrate that the refinement procedure produces excellent approximations to the original periodic eigenvectors.     

Slow viscous flow past a cavity with infinite depth

Two-dimensional slow viscous flow on infinite half-plane past a perpendicular infinite cavity is considered on the basis of the Stokes approximation. Using complex representation of the two-dimensional Stokes flow, the problem is reduced to solving a set of Fredholm integral equations of the second kind. The streamlines and the pressure and vorticity distribution on the wall are numerically determined.     

Field Trial of 40 Gbit/s ETDM Prototype System over 219 km of Installed Single Mode Fiber

Transmission of 40Gbit/s NRZ signal was successfully demonstrated over 219km of installed SMF in KT's Daejeon area network. After transmission, the measured power penalty was 0.5dB for all the tributary channels.     

Multiharmonic-generation biopsy of skin

Because it avoids the in-focus photodamage and phototoxicity problem of two-photon-fluorescence excitation, multiharmonic-generation biopsy based on a 1200-1300-nm light source could provide a truly noninvasive and highly penetrative optical sectioning of skin. We study multiharmonic-generation biopsy of fixed mouse skin. Our preliminary study suggests that this technique could provide submicrometer-resolution deep-tissue noninvasive biopsy images in skin without the use of fluorescence and exogenous markers.     

High resolution feshbach spectroscopy of cesium

We measure high-resolution Feshbach resonance spectra for ultracold cesium atoms colliding in different hyperfine and magnetic sublevels. More than 25 resonances are observed for magnetic fields up to 230 G and their positions are measured with an accuracy down to 0.03 G. From these spectra several ground-state molecular interaction parameters can be extracted with sufficient accuracy to permit for the first time an unambiguous and accurate determination of cesium's ultracold collision properties [P. J. Leo, C. J. Williams, and P. S. Julienne, following Letter, Phys. Rev. Lett. 85, 2721 (2000)].     

Screening possible solid electrolytes by calculating the conduction pathways using Bond Valence method

Inorganic solid electrolytes have distinguished advantages in terms of safety and stability, and are promising to substitute for conventional organic liquid electrolytes. However, low ionic conductivity of typical candidates is the key problem. As connective diffusion path is the prerequisite for high performance, we screen for possible solid electrolytes from the 2004 International Centre for Diffraction Data (ICDD) database by calculating conduction pathways using Bond Valence (BV) method. There are 109846 inorganic crystals in the 2004 ICDD database, and 5295 of them contain lithium. Except for those with toxic, radioactive, rare, or variable valence elements, 1380 materials are candidates for solid electrolytes. The rationality of the BV method is approved by comparing the existing solid electrolytes’ conduction pathways we had calculated with those from experiments or first principle calculations. The implication for doping and substitution, two important ways to improve the conductivity, is also discussed. Among them Li₂CO₃ is selected for a detailed comparison, and the pathway is reproduced well with that based on the density functional studies. To reveal the correlation between connectivity of pathways and conductivity, α/γ-LiAlO₂ and Li₂CO₃ are investigated by the impedance spectrum as an example, and many experimental and theoretical studies are in process to indicate the relationship between property and structure. The BV method can calculate one material within a few minutes, providing an efficient way to lock onto targets from abundant data, and to investigate the structure-property relationship systematically.     

Vacuum ultraviolet 178.7 nm emission in sodium vapour under two-photon resonance excitation

We have observed a fixed wavelength emission at 178.7 nm in sodium vapour under 578.7 nm two-photon resonance excitation. The proposed non-linear wave mixing scheme is described by _{178.7 nm} = 2_L + _{465.7 nm}; where _178.7 is the 178.7 nm photon frequency, _L is the laser-photon frequency, and _465.7 is the 465.7 nm photon frequency. This 465.7 nm emission comes from another six-wave mixing process involving two hyper-electronic Raman scattering photons. The excitation spectrum of the 178.7 nm emission has a typical multiwave mixing pattern with a competing effect appearing at higher temperatures under two-photon resonance excitation. Numerical analysis indicates that this vacuum ultraviolet emission has a poor phase-match condition that will depress the emission intensity to a certain extent. This makes the observation more difficult compared with other reported four-wave mixing generated emissions. Fortunately, on the one hand, it is enhanced by quasi-auto-ionization resonance when the 3s–5s transition is coupled to the sodium continuum by a 330.2 nm photon. On the other hand, its wavelength sits so close to the sodium Cooper minimum that weak absorption will not suppress this vacuum ultraviolet emission further.     

Geometry of the quantum complex projective spaceCP q (N)

We study the constraints from theb→sγ decay in the parameter space of effective supergravities from orbifold string theory and with minimal supesymmetric particle content. Both the general dilaton-dominated universal scenario as well as a non-universal scenario for the soft terms are investigated. It is found that the recently reported CLEO upper and lower bounds constrain the parameter space of the models under scrutiny. In particular we find constraints on the values of the parameter tanβ and the gluino masses. In this class of string scenarios the negative sign of the Higgs mixing parameterμ, is phenomenologically preferred.     

A high‐precision instrument for mapping of rotational errors in rotary stages

A rotational stage is a key component of every X‐ray instrument capable of providing tomographic or diffraction measurements. To perform accurate three‐dimensional reconstructions, runout errors due to imperfect rotation (e.g. circle of confusion) must be quantified and corrected. A dedicated instrument capable of full characterization and circle of confusion mapping in rotary stages down to the sub‐10 nm level has been developed. A high‐stability design, with an array of five capacitive sensors, allows simultaneous measurements of wobble, radial and axial displacements. The developed instrument has been used for characterization of two mechanical stages which are part of an X‐ray microscope.